# If need to close all connections
lapply( dbListConnections( dbDriver( drv = "MySQL")), dbDisconnect)

This is a first pass exploration of different aspects of beer.

Data courtesy of BreweryDB
- Special thanks to Kris Kroski for data ideation and beer

The main question on the table is this:
- Are beer styles actually indicative of shared attributes of the beers within that style? Or are style boundaries more or less arbitrary?
- Two approaches: clustering and prediction
- Clustering: are there natural clusters across the spectum of beers that align well with the styles they’re grouped into?
  - Unsupervised (k-means) clustering based on
    - ABV (alcohol by volume), IBU (international bitterness units), SRM (measure of color)
    - How well do these match up with various “style centers,” defined by mean of ABV, IBU, and SRM per beer style
- Prediction: can we predict a beer’s style based on certain characteristics of the beer?
  - Neural net
  - Random forest
Answer thus far
- Beer-intrinsic attributes aren’t great predictors of style
- Style-defined attributes are the best predictors
  - For instance, the glass a beer is served in (which is defined by its style) is a much better predictor of its style than actual characteristics of the beer like ABV and even the number of different types of hops it contains

Workflow Overview

Hit the BreweryDB API to iteratively pull in all beers and their ingredients along with other things we might want like breweries and glassware
Unnest the JSON responses, including all the ingredients columns, and
Dump this all into a MySQL database
Create a style_collapsed column to reduce the number of levels of our outcome variable
- grep through each beer’s style to determine if that style contains a keyword that qualifies it to be rolled into a collapsed style
- If it does, it gets that keyword in a style_collapsed column
- Further collpase styles that are similar like Hefeweizen and Wit into Wheat
Unnest the ingredients hops and malts into a sparse matrix
- Individual ingredients as columns, beers as rows; cell gets a 1 if ingredient is present and 0 otherwise
Cluster: unsupervised k-means clsutering based on ABV, IBU, and SRM
Run a neural net
- Predict either style or style_collapsed from all the predictors including the total number of hops and malts per beer

Short Aside

The question of what should be a predictor variable for style is a bit murky here. What should be fair game for predicting style and what shouldn’t? Characteristics of a beer that are defined by its style would seem to be “cheating” in a way.

Main candidates are:
- ABV (alcohol by volume), IBU (international bitterness units), SRM (standard reference measure, a scale of beer color from light to dark)
  - These are outputs of a beer that meaningfully define the beer and are theoretically orthogonal to each other
- Ingredients in a beer such as hops and malts
  - Inputs to a beer that have some effect on its flavor profile
  - Semi-cheating because if style is determined beforehand it likely determines at least in part which ingredients are added
- Glass type
  - This is defined entirely by style and is very predictive of it

This document compiled by querying the beer database I built, specifically by sourcing the file read_from_db.R. This is done for expediency’s sake, (the code below detailing how to get the beer, run in full in run_it.R, takes some time to execute).

Get and Prepare Data

Getting beer, the age-old dilemma

The BreweryDB API returns a certain number of results per page; if we want
So, we hit the BreweryDB API and ask for 1:number_of_pages
- We can change number_of_pages to, e.g., 3 if we only want the first 3 pages
- If there’s only one page (as is the case for the glassware endpoing), numberOfPages won’t be returned, so in this case we set number_of_pages to 1
The addition parameter can be an empty string if nothing else is needed

base_url <- "http://api.brewerydb.com/v2"
key_preface <- "/?key="

paginated_request <- function(ep, addition) {    
  full_request <- NULL
  first_page <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                , "&p=1"))
  number_of_pages <- ifelse(!(is.null(first_page$numberOfPages)), 
                            first_page$numberOfPages, 1)      

    for (page in 1:number_of_pages) {                               
    this_request <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                    , "&p=", page, addition),
                             flatten = TRUE) 
    this_req_unnested <- unnest_it(this_request)    #  <- request unnested here
    print(this_req_unnested$currentPage)
    full_request <- bind_rows(full_request, this_req_unnested[["data"]])
  }
  full_request
} 

all_beer_raw <- paginated_request("beers", "&withIngredients=Y")

Function for unnesting JSON used inside paginated_request() below
- Takes the column named name nested within a column in the data portion of the response
  - If the name column doesn’t exist, it takes the first nested column
We use something similar to unnest ingredient like all of a beer’s hops and malts into a long string contained in hops_name and malt_name

unnest_it <- function(df) {
  unnested <- df
  for(col in seq_along(df[["data"]])) {
    if(! is.null(ncol(df[["data"]][[col]]))) {
      if(! is.null(df[["data"]][[col]][["name"]])) {
        unnested[["data"]][[col]] <- df[["data"]][[col]][["name"]]
      } else {
        unnested[["data"]][[col]] <- df[["data"]][[col]][[1]]
      }
    }
  }
  unnested
}

Collapse Styles

Save the most popular styles in keywords
Loop through each keyword
- For each beer, grep through its style column to see if it contains any one of these keywords
- If it does, give it that keyword in a new column style_collapsed
If a beer’s name matches multiple keywords, e.g., American Double India Pale Ale would match Double India Pale Ale, India Pale Ale, and Pale Ale, its style_collapsed is the last of those that appear in keywords
- This is why keywords are intentionally ordered from most general to most specific
- So in the case of an case of American Double India Pale Ale: since Double India Pale Ale appears in keywords after India Pale Ale and Pale Ale, an American Double India Pale Ale would get a style_collapsed of Double India Pale Ale
If no keyword is contained in style, style_collapsed is just whatever’s in style; in other words, it doesn’t get collpsed into a bigger bucket
- This isn’t a huge problem because we’ll pare down to just the most popular styles later, however we could think about creating a catchall “Other” level for style_collapsed

collapse_styles <- function(df) {
  keywords <- c("Lager", "Pale Ale", "India Pale Ale", "Double India Pale Ale", "India Pale Lager", "Hefeweizen", "Barrel-Aged","Wheat", "Pilsner", "Pilsener", "Amber", "Golden", "Blonde", "Brown", "Black", "Stout", "Porter", "Red", "Sour", "Kölsch", "Tripel", "Bitter", "Saison", "Strong Ale", "Barley Wine", "Dubbel", "Altbier")
  
  for (beer in 1:nrow(df)) {
    if (grepl(paste(keywords, collapse="|"), df$style[beer])) {    
      for (keyword in keywords) {         
        if(grepl(keyword, df$style[beer]) == TRUE) {
          df$style_collapsed[beer] <- keyword    
        }                         
      } 
    } else {
      df$style_collapsed[beer] <- as.character(df$style[beer])       
    }
    print(df$style_collapsed[beer])
  }
  return(df)
}

Then we collapse further; right now we just combine all wheaty bears into Wheat and Pils-like beers into Pilsener (with two e’s) by fct_collapseing those levels

collapse_further <- function(df) {
  df[["style_collapsed"]] <- df[["style_collapsed"]] %>%
    fct_collapse(
      "Wheat" = c("Hefeweizen", "Wheat"),
      "Pilsener" = c("Pilsner", "American-Style Pilsener") # pilsener == pilsner == pils
    )
  return(df)
}

Split out Ingredients

When we unnested ingredients, we just concatenated all of the ingredients for a given beer into a long string
If we want, we can split out the ingredients that were concatenated in <ingredient>_name with this split_ingredients function
This takes a vector of ingredients_to_split, so e.g. c("hops_name", "malt_name") and creates one column for each type of ingredient (hops_name_1, hops_name_2, etc.)
We str_split on the ingredient and get a list back
We find the max number of instances of an ingredient per beer, which will be the number of columns we’re adding
For each new column we need, we create it, initialize it with NAs, and name it
Then for each element in our list of split up ingredients, if it exists, we add it to the correct column in our df

split_ingredients <- function(df, ingredients_to_split) {
  
  ncol_df <- ncol(df)
  
  for (ingredient in ingredients_to_split) {

    ingredient_split <- str_split(df[[ingredient]], ", ")    
    num_new_cols <- max(lengths(ingredient_split))    
  
    for (num in 1:num_new_cols) {
      
      this_col <- ncol_df + 1         
      
      df[, this_col] <- NA
      names(df)[this_col] <- paste0(ingredient, "_", num)
      ncol_df <- ncol(df)             
      for (row in seq_along(ingredient_split)) {          
        if (!is.null(ingredient_split[[row]][num])) {        
          df[row, this_col] <- ingredient_split[[row]][num]
        }
      }
      df[[names(df)[this_col]]] <- factor(df[[names(df)[this_col]]])
    }
    
    ncol_df <- ncol(df)
  }
  return(df)
}

Find the Most Popualar Styles

Find mean ABV, IBU, and SRM per collapsed style
Arrange collapsed styles by the number of beers that fall into them
- This is of course dependent on how we collapse styles

library(forcats)

# Pare down to only cases where style is not NA
beer_dat <- beer_necessities

beer_dat_pared <- beer_dat[complete.cases(beer_dat$style), ]

# Arrange beer dat by style popularity
style_popularity <- beer_dat_pared %>% 
  group_by(style) %>% 
  count() %>% 
  arrange(desc(n))
style_popularity

# Add a column that scales popularity
style_popularity <- bind_cols(style_popularity, 
                               n_scaled = as.vector(scale(style_popularity$n)))

# Find styles that are above a z-score of 0
popular_styles <- style_popularity %>% 
  filter(n_scaled > 0)

# Pare dat down to only beers that fall into those styles
popular_beer_dat <- beer_dat_pared %>% 
  filter(
    style %in% popular_styles$style
  ) %>% 
  droplevels() %>% 
  as_tibble() 
nrow(popular_beer_dat)

# Find the centers (mean abv, ibu, srm) of the most popular styles
style_centers <- popular_beer_dat %>% 
  group_by(style_collapsed) %>% 
  add_count() %>% 
  summarise(
    mean_abv = mean(abv, na.rm = TRUE),
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_srm = mean(srm, na.rm = TRUE),
    n = median(n, na.rm = TRUE)          # Median here only for summarise. Should be just the same as n
  ) %>% 
  arrange(desc(n)) %>% 
  drop_na() %>% 
  droplevels()

# Give some nicer names
style_centers_rename <- style_centers %>% 
  rename(
    `Collapsed Style` = style_collapsed,
    `Mean ABV` = mean_abv,
    `Mean IBU` = mean_ibu,
    `Mean SRM` = mean_srm,
    `Numer of Beers` = n
  )

Take a look at the table

kable(style_centers_rename)

Collapsed Style	Mean ABV	Mean IBU	Mean SRM	Numer of Beers
India Pale Ale	6.578468	66.04268	9.989313	6524
Pale Ale	5.695480	40.86930	8.890306	4280
Stout	7.991841	43.89729	36.300000	4238
Wheat	5.158040	17.47168	5.861842	3349
Double India Pale Ale	8.930599	93.48142	11.006873	2525
Red	5.742565	33.81127	16.178862	2521
Lager	5.453718	30.64361	8.457447	2230
Saison	6.400189	27.25114	7.053476	2167
Blonde	5.595298	22.39432	5.625000	2044
Porter	6.182049	33.25369	32.197605	1973
Brown	6.159212	32.21577	23.592000	1462
Pilsener	5.227593	33.51346	4.413462	1268
Specialty Beer	6.446402	33.77676	15.520548	1044
Bitter	5.322364	38.28175	12.460526	939
Fruit Beer	5.195222	19.24049	8.666667	905
Herb and Spice Beer	6.621446	27.77342	18.166667	872
Sour	6.224316	18.88869	10.040816	797
Strong Ale	8.826425	36.74233	22.547945	767
Tripel	9.029775	32.51500	7.680556	734
Black	6.958714	65.50831	31.080000	622
Barley Wine	10.781600	74.04843	19.561404	605
Kölsch	4.982216	23.37183	4.371795	593
Barrel-Aged	9.002506	39.15789	18.133333	540
Other Belgian-Style Ales	7.516318	37.55812	17.549020	506
Pumpkin Beer	6.712839	23.48359	17.918033	458
Dubbel	7.509088	25.05128	22.940000	399
Scotch Ale	7.620233	26.36909	24.222222	393
German-Style Doppelbock	8.045762	28.88692	25.696970	376
Fruit Cider	6.205786	25.60000	12.000000	370
German-Style Märzen	5.746102	25.63796	14.322581	370

Now that the munging is done, onto the main question: do natural clusters in beer align with style boundaries?

Ingredients

To get more granular with ingredients, we can split out each individual ingredient into its own column. If a beer or style contains that ingredient, its row gets a 1 in that ingredient column and a 0 otherwise.

From this, we can find the total number of hops and malts per grouper.

The dataframe we’ll use will be beer_necessities

This function takes a dataframe and two other parameters set at the outset:
- ingredient_want: this can be hops, malt, or other ingredients like yeast if we pull that in
- grouper: can be a vector of one or more things to group by, like beer name or style

pick_ingredient_get_beer <- function (ingredient_want, df, grouper) {
  
  # ----------------------- Setup --------------------------- #
  # We've already split ingredient number names out from the concatenated string into columns like `malt_name_1`,
  # `malt_name_2`, etc. We need to find the range of these columns; there will be a different number of malt
  # columns than hops columns, for instance. The first one will be `<ingredient>_name_1` and from this we can find
  # the index of this column in our dataframe. We get the name of last one with the `get_last_ing_name_col()`
  # function. Then we save a vector of all the ingredient column names in `ingredient_colnames`. It will stay
  # constant even if the indices change when we select out certain columns. 
  
  # First ingredient
  first_ingredient_name <- paste(ingredient_want, "_name_1", sep="")
  first_ingredient_index <- which(colnames(df)==first_ingredient_name)
  
  # Get the last ingredient
  get_last_ing_name_col <- function(df) {
    for (col in names(df)) {
      if (grepl(paste(ingredient_want, "_name_", sep = ""), col) == TRUE) {
        name_last_ing_col <- col
      }
    }
    return(name_last_ing_col)
  }
  
  # Last ingredient
  last_ingredient_name <- get_last_ing_name_col(df)
  last_ingredient_index <- which(colnames(df)==last_ingredient_name)
  
  # Vector of all the ingredient column names
  ingredient_colnames <- names(df)[first_ingredient_index:last_ingredient_index]
  
  # Non-ingredient column names we want to keep
  to_keep_col_names <- c("cluster_assignment", "name", "abv", "ibu", "srm", "style", "style_collapsed")
  
  # -------------------------------------------------------------------------------# 
  
  # Inside `gather_ingredients()` we take out superflous column names that are not in `to_keep_col_names` or one 
  # of the ingredient columns, find what the new ingredient column indices are, since they'll have changed after 
  # we pared down and then gather all of the ingredient columns (e.g., `hops_name_1`) into one long column, 
  # `ing_keys` and all the actual ingredient names (e.g., Cascade) into `ing_names`.
  
  # ----------------------------- Gather columns --------------------------------- #
  gather_ingredients <- function(df, cols_to_gather) {
    to_keep_indices <- which(colnames(df) %in% to_keep_col_names)
    
    selected_df <- df[, c(to_keep_indices, first_ingredient_index:last_ingredient_index)]
    
    new_ing_indices <- which(colnames(selected_df) %in% cols_to_gather)    # indices will have changed since we pared down 
    
    df_gathered <- selected_df %>%
      gather_(
        key_col = "ing_keys",
        value_col = "ing_names",
        gather_cols = colnames(selected_df)[new_ing_indices]
      ) %>%
      mutate(
        count = 1
      )
    df_gathered
  }
  beer_gathered <- gather_ingredients(df, ingredient_colnames)  # ingredient colnames defined above function
  # ------------------------------------------------------------------------------- # 
  
  # Next we get a vector of all ingredient levels and take out the one that's an empty string and 
  # use this vector of ingredient levels in `select_spread_cols()` below
  # Get a vector of all ingredient levels
  beer_gathered$ing_names <- factor(beer_gathered$ing_names)
  ingredient_levels <- levels(beer_gathered$ing_names) 
  
  # Take out the level that's just an empty string
  to_keep_levels <- !(c(1:length(ingredient_levels)) %in% which(ingredient_levels == ""))
  ingredient_levels <- ingredient_levels[to_keep_levels]
  
  beer_gathered$ing_names <- as.character(beer_gathered$ing_names)
  
  # ----------------------------------------------------------------------------- # 
  
  # Then we spread the ingredient names: we take what was previously the `value` in our gathered dataframe, the
  # actual ingredient names (Cascade, Centennial) and make that our `key`; it'll form the new column names. The
  # new `value` is `value` is count; it'll populate the row cells. If a given row has a certain ingredient, it
  # gets a 1 in the corresponding cell, an NA otherwise. 
  # We add a unique idenfitier for each row with `row`, which we'll drop later (see [Hadley's SO
  # comment](https://stackoverflow.com/questions/25960394/unexpected-behavior-with-tidyr)).
  
  # ------------------------------- Spread columns -------------------------------- #
  spread_ingredients <- function(df) {
    df_spread <- df %>% 
      mutate(
        row = 1:nrow(df)        # Add a unique idenfitier for each row which we'll need in order to spread; we'll drop this later
      ) %>%                                 
      spread(
        key = ing_names,
        value = count
      ) 
    return(df_spread)
  }
  beer_spread <- spread_ingredients(beer_gathered)
  # ------------------------------------------------------------------------------- # 
  
  # ------------------------- Select only certain columns ------------------------- #
  select_spread_cols <- function(df) {
    to_keep_col_indices <- which(colnames(df) %in% to_keep_col_names)
    to_keep_ingredient_indices <- which(colnames(df) %in% ingredient_levels)
    
    to_keep_inds_all <- c(to_keep_col_indices, to_keep_ingredient_indices)
    
    new_df <- df %>% 
      select_(
        .dots = to_keep_inds_all
      )
    return(new_df)
  }
  beer_spread_selected <- select_spread_cols(beer_spread)
  # ------------------------------------------------------------------------------- # 
  # Take out all rows that have no ingredients specified at all
  inds_to_remove <- apply(beer_spread_selected[, first_ingredient_index:last_ingredient_index], 
                          1, function(x) all(is.na(x)))
  beer_spread_no_na <- beer_spread_selected[ !inds_to_remove, ]
  
  
  # ----------------- Group ingredients by the grouper specified ------------------- #
  # Then we do the final step and group by the groupers.
  
  get_ingredients_per_grouper <- function(df, grouper = grouper) {
    df_grouped <- df %>%
      ungroup() %>% 
      group_by_(grouper)
    
    not_for_summing <- which(colnames(df_grouped) %in% to_keep_col_names)
    max_not_for_summing <- max(not_for_summing)
    
    per_grouper <- df_grouped %>% 
      select(-c(abv, ibu, srm)) %>%    # taking out temporarily
      summarise_if(
        is.numeric,              
        sum, na.rm = TRUE
        # -c(abv, ibu, srm)
      ) %>%
      mutate(
        total = rowSums(.[(max_not_for_summing + 1):ncol(.)], na.rm = TRUE)    
      )
    
    # Send total to the second position
    per_grouper <- per_grouper %>% 
      select(
        name, total, everything()
      )
    
    # Replace total column with more descriptive name: total_<ingredient>
    names(per_grouper)[which(names(per_grouper) == "total")] <- paste0("total_", ingredient_want)
    
    return(per_grouper)
  }
  # ------------------------------------------------------------------------------- # 
  
  ingredients_per_grouper <- get_ingredients_per_grouper(beer_spread_selected, grouper)
  return(ingredients_per_grouper)
}

Now run the function with ingredient_want as first hops, then malt
Then join the resulting dataframes and remove/reorder some columns

# Run the entire function with ingredient_want set to hops, grouping by name
ingredients_per_beer_hops <- pick_ingredient_get_beer(ingredient_want = "hops", 
                                                      beer_necessities, 
                                                      grouper = c("name", "style_collapsed"))
# Same for malt
ingredients_per_beer_malt <- pick_ingredient_get_beer(ingredient_want = "malt", 
                                                      beer_necessities, 
                                                      grouper = c("name", "style_collapsed"))
# Join those on our original dataframe by name
beer_ingredients_join_first_ingredient <- left_join(beer_necessities, ingredients_per_beer_hops,
                                                    by = "name")
beer_ingredients_join <- left_join(beer_ingredients_join_first_ingredient, ingredients_per_beer_malt,
                                   by = "name")
# Take out some unnecessary columns
unnecessary_cols <- c("styleId", "abv_scaled", "ibu_scaled", "srm_scaled", 
                      "hops_id", "malt_id", "glasswareId", "style.categoryId")
beer_ingredients_join <- beer_ingredients_join[, (! names(beer_ingredients_join) %in% unnecessary_cols)]
# If we also want to take out any of the malt_name_1, malt_name_2, etc. columns we can do this with a grep
more_unnecessary <- c("hops_name_|malt_name_")
beer_ingredients_join <- 
  beer_ingredients_join[, (! grepl(more_unnecessary, names(beer_ingredients_join)) == TRUE)]
# Reorder columns a bit
beer_ingredients_join <- beer_ingredients_join %>% 
  select(
    id, name, total_hops, total_malt, everything(), -description
  )
# And get a df that includes total_hops and total_malt but not all the other ingredient columns
beer_totals <- beer_ingredients_join %>% 
  select(
    id, name, total_hops, total_malt, style, style_collapsed,
    abv, ibu, srm, glass, hops_name, malt_name
  )

Now we’re left with something of a sparse matrix of all the ingredients compared to all the beers

kable(beer_ingredients_join[1:20, ])

id	name	total_hops	total_malt	style	abv	ibu	srm	glass	hops_name	malt_name	style_collapsed	Cascade	Perle (American)	Saaz (American)	Sterling	Barley - Malted	Chocolate Malt	Honey Malt	Munich Malt	Oats - Flaked	Two-Row Pale Malt
cBLTUw	"18" Imperial IPA 2	0	0	American-Style Imperial Stout	11.10	NA	33	Pint	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
ZsQEJt	"633" American Pale Ale	0	0	American-Style Pale Ale	6.33	25.0	NA	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
tmEthz	"Admiral" Stache	2	4	Baltic-Style Porter	7.00	23.0	37	Pint	Perle (American), Saaz (American)	Barley - Malted, Chocolate Malt, Munich Malt, Oats - Flaked	Porter	0	1	1	0	1	1	0	1	1	0
b7SfHG	"Ah Me Joy" Porter	0	0	Robust Porter	5.40	51.0	40	NA	NA	NA	Porter	0	0	0	0	0	0	0	0	0	0
zcJMId	"Alternating Currant" Sour	0	0	American-Style Sour Ale	4.80	12.0	NA	NA	NA	NA	Sour	0	0	0	0	0	0	0	0	0	0
UM8GL6	"B" Street Pineapple Blonde	0	0	Golden or Blonde Ale	4.60	NA	5	NA	NA	NA	Blonde	0	0	0	0	0	0	0	0	0	0
NIaY9C	"B.B. Rodriguez" Double Brown	0	0	American-Style Brown Ale	8.50	30.0	NA	NA	NA	NA	Brown	0	0	0	0	0	0	0	0	0	0
PBEXhV	"Bison Eye Rye" Pale Ale \| 2 of 4 Part Pale Ale Series	0	0	American-Style Pale Ale	5.80	51.0	8	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
wRmmdv	"California Crude" Black IPA	0	0	American-Style Black Ale	7.60	80.0	NA	NA	NA	NA	Black	0	0	0	0	0	0	0	0	0	0
EPYNpW	"C’est Noir" Imperial Stout	0	0	British-Style Imperial Stout	10.80	70.0	NA	NA	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
AXmvOd	"Dust Up" Cloudy Pale Ale \| 1 of 4 Part Pale Ale Series	0	0	American-Style Pale Ale	5.40	54.0	11	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
c5pZg5	"EVL1" Imperial Red Ale	0	0	Imperial Red Ale	10.40	64.0	NA	NA	NA	NA	Red	0	0	0	0	0	0	0	0	0	0
xBKAka	"Galactic Wrath" IPA	0	0	American-Style India Pale Ale	7.50	75.0	NA	NA	NA	NA	India Pale Ale	0	0	0	0	0	0	0	0	0	0
Hr5A0t	"God Country" Kolsch	0	0	German-Style Kölsch / Köln-Style Kölsch	5.60	28.2	5	NA	NA	NA	Kölsch	0	0	0	0	0	0	0	0	0	0
UjFyXJ	"Hey Victor" Smoked Porter	0	0	Smoke Beer (Lager or Ale)	5.50	NA	NA	NA	NA	NA	Lager	0	0	0	0	0	0	0	0	0	0
5UcMBc	"Ignition" IPA	0	0	American-Style India Pale Ale	6.60	45.0	NA	Pint	NA	NA	India Pale Ale	0	0	0	0	0	0	0	0	0	0
mrVjY4	"Jemez Field Notes" Golden Lager	0	0	Golden or Blonde Ale	4.90	20.0	5	NA	NA	NA	Blonde	0	0	0	0	0	0	0	0	0	0
54rSgo	"Jemmy Dean" Breakfast Stout	0	0	Sweet or Cream Stout	NA	NA	NA	Pint	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
JsKjkk	"Mauvaises Choses"	0	0	Belgian-Style Pale Strong Ale	7.00	30.0	NA	Tulip	NA	NA	Strong Ale	0	0	0	0	0	0	0	0	0	0
b7WWL6	"Mike Saw a Sasquatch" Session Ale	2	2	Golden or Blonde Ale	4.70	26.0	NA	Pint	Cascade, Sterling	Honey Malt, Two-Row Pale Malt	Blonde	1	0	0	1	0	0	1	0	0	1

Unsupervised Clustering

We K-means cluster beers based on certain numeric predictor variables.

Prep

Write a funciton that takes a dataframe, a set of predictors, a response variable, and the number of cluster centers you want
- NB: There are not not very many beers have SRM so we may not want to omit based on it
Take out missing values, and scale the data
Take out outliers, defined as beers have to have an ABV between 3 and 20 and an IBU less than 200
Then cluster on just the predictors and compare to the response variable

library(NbClust)
cluster_it <- function(df, preds, to_scale, resp, n_centers) {
  df_for_clustering <- df %>%
    select_(.dots = c(response_vars, cluster_on)) %>%
    na.omit() %>%
    filter(
      abv < 20 & abv > 3
    ) %>%
    filter(
      ibu < 200
    )
  df_all_preds <- df_for_clustering %>%
    select_(.dots = preds)
  df_preds_scale <- df_all_preds %>%
    select_(.dots = to_scale) %>%
    rename(
      abv_scaled = abv,
      ibu_scaled = ibu,
      srm_scaled = srm
    ) %>%
    scale() %>%
    as_tibble()
  df_preds <- bind_cols(df_preds_scale, df_all_preds[, (!names(df_all_preds) %in% to_scale)])
  df_outcome <- df_for_clustering %>%
    select_(.dots = resp) %>%
    na.omit()
  set.seed(9)
  clustered_df_out <- kmeans(x = df_preds, centers = n_centers, trace = TRUE)
  clustered_df <- as_tibble(data.frame(
    cluster_assignment = factor(clustered_df_out$cluster),
    df_outcome, df_preds,
    df_for_clustering %>% select(abv, ibu, srm)))
  return(clustered_df)
}

Cluster

First we’ll run the fuction with 10 centers, and cluster on the predictors ABV, IBU, SRM, total_hops, and total_malt.

cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")
clustered_beer <- cluster_it(df = beer_totals,
                             preds = cluster_on,
                             to_scale = to_scale,
                             resp = response_vars,
                             n_centers = 10)

KMNS(*, k=10): iter=  1, indx=5
 QTRAN(): istep=4472, icoun=1
 QTRAN(): istep=8944, icoun=84
 QTRAN(): istep=13416, icoun=31
 QTRAN(): istep=17888, icoun=310
 QTRAN(): istep=22360, icoun=444
 QTRAN(): istep=26832, icoun=3571
KMNS(*, k=10): iter=  2, indx=28
 QTRAN(): istep=4472, icoun=3
 QTRAN(): istep=8944, icoun=26
 QTRAN(): istep=13416, icoun=0
 QTRAN(): istep=17888, icoun=45
 QTRAN(): istep=22360, icoun=37
 QTRAN(): istep=26832, icoun=170
 QTRAN(): istep=31304, icoun=45
 QTRAN(): istep=35776, icoun=64
 QTRAN(): istep=40248, icoun=692
KMNS(*, k=10): iter=  3, indx=6
 QTRAN(): istep=4472, icoun=16
 QTRAN(): istep=8944, icoun=36
 QTRAN(): istep=13416, icoun=318
 QTRAN(): istep=17888, icoun=1114
 QTRAN(): istep=22360, icoun=1628
 QTRAN(): istep=26832, icoun=1518
KMNS(*, k=10): iter=  4, indx=227
 QTRAN(): istep=4472, icoun=560
 QTRAN(): istep=8944, icoun=1426
 QTRAN(): istep=13416, icoun=401
KMNS(*, k=10): iter=  5, indx=4472

Head of the clustering data

kable(clustered_beer[1:20, ])

cluster_assignment	name	style	style_collapsed	abv_scaled	ibu_scaled	srm_scaled	total_hops	total_malt	abv	ibu	srm
3	"Admiral" Stache	Baltic-Style Porter	Porter	0.2915030	-0.6641211	2.1990458	0.4954773	1.1342326	7.0	23.0	37
3	"Ah Me Joy" Porter	Robust Porter	Porter	-0.5813196	0.4600343	2.4832200	-0.1956564	-0.2062241	5.4	51.0	40
10	"Bison Eye Rye" Pale Ale \| 2 of 4 Part Pale Ale Series	American-Style Pale Ale	Pale Ale	-0.3631139	0.4600343	-0.5479716	-0.1956564	-0.2062241	5.8	51.0	8
10	"Dust Up" Cloudy Pale Ale \| 1 of 4 Part Pale Ale Series	American-Style Pale Ale	Pale Ale	-0.5813196	0.5804795	-0.2637974	-0.1956564	-0.2062241	5.4	54.0	11
2	"God Country" Kolsch	German-Style Kölsch / Köln-Style Kölsch	Kölsch	-0.4722168	-0.4553494	-0.8321458	-0.1956564	-0.2062241	5.6	28.2	5
2	"Jemez Field Notes" Golden Lager	Golden or Blonde Ale	Blonde	-0.8540767	-0.7845663	-0.8321458	-0.1956564	-0.2062241	4.9	20.0	5
2	#10 Hefewiezen	South German-Style Hefeweizen / Hefeweissbier	Wheat	-0.7449738	-1.1459020	-0.9268705	-0.1956564	-0.2062241	5.1	11.0	4
2	#9	American-Style Pale Ale	Pale Ale	-0.7449738	-0.7845663	-0.4532468	0.4954773	0.4640043	5.1	20.0	9
2	#KoLSCH	German-Style Kölsch / Köln-Style Kölsch	Kölsch	-0.9086281	-0.5035275	-1.0215953	-0.1956564	-0.2062241	4.8	27.0	3
2	'Inappropriate' Cream Ale	American-Style Cream Ale or Lager	Lager	-0.6358710	-0.8648631	-0.8321458	-0.1956564	-0.2062241	5.3	18.0	5
10	'tis the Saison	French & Belgian-Style Saison	Saison	0.2915030	-0.3830822	-0.6426963	-0.1956564	-0.2062241	7.0	30.0	7
2	(306) URBAN WHEAT BEER	Belgian-Style White (or Wit) / Belgian-Style Wheat	Wheat	-0.7995252	-0.7845663	-0.4532468	-0.1956564	-0.2062241	5.0	20.0	9
7	(512) ALT	German-Style Altbier	Altbier	-0.2540111	-0.1421918	0.6834500	0.1499105	0.7991185	6.0	36.0	21
7	(512) Bruin (A.K.A. Brown Bear)	American-Style Brown Ale	Brown	0.6188115	-0.3830822	0.6834500	0.1499105	1.1342326	7.6	30.0	21
9	(512) FOUR	Strong Ale	Strong Ale	0.5642601	-0.1823402	-0.5479716	0.8410441	1.1342326	7.5	35.0	8
5	(512) IPA	American-Style India Pale Ale	India Pale Ale	0.2915030	1.0221120	-0.5479716	0.8410441	0.7991185	7.0	65.0	8
9	(512) ONE	Belgian-Style Pale Strong Ale	Strong Ale	0.8370171	-0.7042695	-0.5479716	-0.1956564	0.4640043	8.0	22.0	8
10	(512) Pale	American-Style Pale Ale	Pale Ale	-0.2540111	-0.3830822	-0.6426963	0.8410441	0.7991185	6.0	30.0	7
6	(512) SIX	Belgian-Style Dubbel	Dubbel	0.5642601	-0.5838243	1.3465231	0.4954773	0.7991185	7.5	25.0	28
9	(512) THREE	Belgian-Style Tripel	Tripel	1.6552883	-0.7042695	-0.3585221	0.1499105	0.7991185	9.5	22.0	10

Join the clustered beer on beer_ingredients_join

beer_ingredients_join_clustered <- left_join(beer_ingredients_join, clustered_beer, 
                                             by = "name")

A table of cluster counts broken down by style

cluster_table_counts <- table(style = clustered_beer$style_collapsed, cluster = clustered_beer$cluster_assignment)
kable(cluster_table_counts)

	1	2	3	4	5	6	7	8	9	10
Adambier	0	0	0	0	0	0	0	0	0	0
Altbier	0	0	1	0	2	1	11	0	0	7
Amber	0	9	0	0	1	0	4	0	0	3
American-Style Malt Liquor	0	1	0	0	0	0	0	0	1	0
American-Style Märzen / Oktoberfest	0	5	0	0	0	0	6	11	1	2
Apple Wine	0	0	0	0	0	0	0	0	0	0
Bamberg-Style Bock Rauchbier	0	0	0	0	0	0	1	0	0	0
Bamberg-Style Helles Rauchbier	0	0	0	0	0	0	0	0	0	0
Bamberg-Style Märzen Rauchbier	0	0	0	0	0	0	3	0	0	0
Bamberg-Style Weiss (Smoke) Rauchbier (Dunkel or Helles)	0	2	1	0	0	0	1	0	0	1
Barley Wine	28	0	0	19	2	2	0	0	11	0
Barrel-Aged	9	2	3	2	1	8	4	0	16	3
Belgian-style Fruit Beer	0	2	0	0	0	0	0	0	0	0
Belgian-Style Fruit Lambic	0	0	0	0	1	1	2	0	0	0
Belgian-Style Gueuze Lambic	0	0	0	0	0	0	0	0	0	0
Belgian-Style Lambic	0	2	0	0	0	0	0	0	0	0
Belgian-Style Quadrupel	10	0	0	0	0	9	0	0	8	0
Belgian-Style Table Beer	0	5	0	0	0	0	1	0	0	0
Bitter	1	15	0	0	2	1	22	0	1	38
Black	0	0	8	4	6	24	1	0	0	0
Blonde	0	113	1	0	1	1	4	0	19	21
Braggot	0	1	0	0	0	1	0	0	1	0
Brett Beer	0	1	0	1	0	1	0	0	2	2
Brown	2	8	28	1	6	11	90	0	0	2
California Common Beer	0	1	1	0	0	0	2	0	0	8
Chili Pepper Beer	0	5	0	0	0	0	2	0	0	3
Chocolate / Cocoa-Flavored Beer	0	1	3	0	0	0	2	0	0	2
Coffee-Flavored Beer	0	0	9	0	2	8	1	0	0	0
Common Cider	0	0	0	0	0	0	0	0	0	0
Common Perry	0	0	0	0	0	0	0	0	0	0
Contemporary Gose	0	9	1	0	0	0	0	0	0	0
Cyser (Apple Melomel)	0	0	0	0	0	0	0	0	0	0
Dark American-Belgo-Style Ale	0	0	0	0	0	2	1	0	0	0
Dortmunder / European-Style Export	0	3	0	0	0	0	1	0	0	4
Double India Pale Ale	5	0	0	179	40	3	0	0	5	0
Dry Mead	0	0	0	0	0	0	0	0	0	0
Dubbel	0	0	2	0	1	13	15	0	10	0
Dutch-Style Kuit, Kuyt or Koyt	0	0	0	0	0	0	0	0	0	1
Energy Enhanced Malt Beverage	0	0	0	0	0	0	0	0	0	0
English Cider	0	0	0	0	0	0	0	0	0	0
English-Style Dark Mild Ale	0	1	2	0	0	1	3	0	0	0
English-Style Pale Mild Ale	0	6	1	0	1	0	4	0	0	2
English-Style Summer Ale	0	11	0	0	0	0	0	0	0	1
European-Style Dark / Münchner Dunkel	0	0	2	0	0	0	8	0	0	0
Field Beer	0	1	0	0	1	0	4	0	0	5
Flavored Malt Beverage	0	3	0	0	0	0	0	0	0	0
French Cider	0	0	0	0	0	0	0	0	0	0
French-Style Bière de Garde	0	1	0	0	0	0	4	0	6	3
Fresh "Wet" Hop Ale	0	0	0	0	8	0	0	0	0	6
Fruit Beer	1	36	2	0	4	0	6	0	5	2
Fruit Cider	0	0	0	0	0	0	1	0	0	0
German-Style Doppelbock	0	0	2	0	0	13	5	0	9	0
German-Style Eisbock	0	0	0	0	0	0	0	0	1	0
German-Style Heller Bock/Maibock	0	1	1	0	1	0	6	0	4	9
German-Style Leichtbier	0	1	0	0	0	0	0	0	0	0
German-Style Leichtes Weizen / Weissbier	0	4	0	0	0	0	0	0	0	0
German-Style Märzen	0	8	0	0	0	0	10	11	0	1
German-Style Oktoberfest / Wiesen (Meadow)	0	3	0	0	0	0	2	3	1	1
German-Style Rye Ale (Roggenbier) with or without Yeast	0	1	1	0	0	1	2	0	0	0
German-Style Schwarzbier	0	0	14	0	0	1	3	0	0	0
Ginjo Beer or Sake-Yeast Beer	0	0	0	0	0	0	0	0	0	0
Gluten-Free Beer	0	1	0	0	1	0	1	0	0	0
Grodziskie	0	2	0	0	0	0	0	0	0	0
Herb and Spice Beer	1	12	9	0	7	6	12	0	4	4
Historical Beer	0	6	1	0	0	0	1	0	0	1
India Pale Ale	0	5	3	38	402	8	5	15	2	99
Kellerbier (Cellar beer) or Zwickelbier - Ale	0	2	0	0	0	0	0	0	0	2
Kölsch	0	67	0	0	1	0	1	0	0	3
Lager	1	132	6	6	24	8	51	0	9	30
Leipzig-Style Gose	0	12	0	0	0	0	0	0	0	1
Metheglin	0	0	0	0	0	0	0	0	0	0
Mixed Culture Brett Beer	0	0	0	0	0	0	0	0	1	0
Münchner (Munich)-Style Helles	0	32	1	0	0	0	1	0	0	0
New England Cider	0	0	0	0	0	0	0	0	0	0
Non-Alcoholic (Beer) Malt Beverages	0	0	0	0	0	0	0	0	0	0
Old Ale	7	0	0	0	1	4	2	0	5	1
Open Category Mead	0	0	0	0	0	0	0	0	0	0
Other Belgian-Style Ales	0	3	4	1	8	5	7	0	6	5
Other Fruit Melomel	0	0	0	0	0	0	0	0	0	0
Other Specialty Cider or Perry	0	0	0	0	0	0	0	0	0	0
Pale Ale	1	52	1	1	51	5	28	19	11	229
Pale American-Belgo-Style Ale	0	1	0	0	3	0	1	0	1	4
Pilsener	0	69	0	1	4	1	1	0	1	59
Porter	1	0	121	0	0	32	28	0	1	1
Pumpkin Beer	1	7	5	0	0	4	18	0	8	3
Pyment (Grape Melomel)	0	0	0	0	0	0	0	0	0	0
Red	0	25	15	13	28	13	125	7	7	40
Saison	0	53	3	0	2	1	7	0	31	42
Scotch Ale	0	0	4	0	0	12	9	0	7	1
Scottish-Style Export Ale	0	1	0	0	0	0	4	0	0	0
Scottish-Style Heavy Ale	0	0	1	0	0	7	2	0	4	0
Scottish-Style Light Ale	0	1	0	0	0	0	3	0	0	0
Semi-Sweet Mead	0	0	0	0	0	0	0	0	0	0
Session Beer	0	17	0	0	2	0	0	0	0	18
Sour	1	19	2	0	1	4	4	0	2	4
South German-Style Bernsteinfarbenes Weizen / Weissbier	0	1	0	0	0	0	0	0	0	0
South German-Style Dunkel Weizen / Dunkel Weissbier	0	0	0	0	0	1	13	0	1	0
South German-Style Kristall Weizen / Kristall Weissbier	0	1	0	0	0	0	0	0	0	0
South German-Style Weizenbock / Weissbock	0	1	0	0	0	0	0	0	4	1
Specialty Beer	0	15	9	1	5	5	14	0	11	5
Stout	27	2	114	0	1	50	3	0	3	3
Strong Ale	6	0	2	4	3	16	4	0	45	2
Sweet Mead	0	0	0	0	0	0	0	0	0	0
Traditional German-Style Bock	0	1	4	0	0	3	11	0	2	5
Traditional Perry	0	0	0	0	0	0	0	0	0	0
Tripel	1	0	0	2	0	3	0	0	58	1
Wheat	0	266	3	0	4	1	13	0	12	18
Wild Beer	0	3	0	0	0	0	0	0	1	1

Plot the clusters. There are 3 axes: ABV, IBU, and SRM, so we choose two at a time.

clustered_beer_plot_abv_ibu <- ggplot(data = clustered_beer, aes(x = abv, y = ibu, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_ibu

clustered_beer_plot_abv_srm <- ggplot(data = clustered_beer, aes(x = abv, y = srm, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "SRM") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_srm

Now we can add in the style centers (means) for each style_collapsed and label it.

library(ggrepel)
abv_ibu_clusters_vs_style_centers <- ggplot() +   
  geom_point(data = clustered_beer, 
             aes(x = abv, y = ibu, colour = cluster_assignment), alpha = 0.5) +
  geom_point(data = style_centers,
             aes(mean_abv, mean_ibu), colour = "black") +
  geom_text_repel(data = style_centers, aes(mean_abv, mean_ibu, label = style_collapsed), 
                  box.padding = unit(0.45, "lines"),
                  family = "Calibri",
                  label.size = 0.3) +
  ggtitle("Popular Styles vs. k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment") +
  theme_bw()
abv_ibu_clusters_vs_style_centers

The clustering above used a smaller number of clusters (10) than there are styles_collapsed. That makes it difficult to determine whether a given style fits snugly into a cluster or not.

Cluster on just certain selected styles

We’ll take five very distinct collapsed styles and re-run the clustering on beers that fall into these categories. These styles were intentionally chosen because they are quite distinct: Blonde, IPA, Stout, Tripel, Wheat. Arguably, of these five styles Blondes and Wheats are the closest

styles_to_keep <- c("Blonde", "India Pale Ale", "Stout", "Tripel", "Wheat")
bt_certain_styles <- beer_totals %>%
  filter(
    style_collapsed %in% styles_to_keep
  )
cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")
certain_styles_clustered <- cluster_it(df = bt_certain_styles,
                                 preds = cluster_on,
                                 to_scale = to_scale,
                                 resp = response_vars,
                                 n_centers = 5)

KMNS(*, k=5): iter=  1, indx=4
 QTRAN(): istep=1322, icoun=2
 QTRAN(): istep=2644, icoun=20
 QTRAN(): istep=3966, icoun=96
 QTRAN(): istep=5288, icoun=0
 QTRAN(): istep=6610, icoun=13
 QTRAN(): istep=7932, icoun=285
KMNS(*, k=5): iter=  2, indx=13
 QTRAN(): istep=1322, icoun=147
 QTRAN(): istep=2644, icoun=138
 QTRAN(): istep=3966, icoun=20
 QTRAN(): istep=5288, icoun=599
KMNS(*, k=5): iter=  3, indx=20
 QTRAN(): istep=1322, icoun=146
 QTRAN(): istep=2644, icoun=617
KMNS(*, k=5): iter=  4, indx=1322

style_centers_certain_styles <- style_centers %>% 
  filter(style_collapsed %in% styles_to_keep)

Table of style vs. cluster.

kable(table(style = certain_styles_clustered$style_collapsed, cluster = certain_styles_clustered$cluster_assignment))

	1	2	3	4	5
Adambier	0	0	0	0	0
Altbier	0	0	0	0	0
Amber	0	0	0	0	0
American-Style Malt Liquor	0	0	0	0	0
American-Style Märzen / Oktoberfest	0	0	0	0	0
Apple Wine	0	0	0	0	0
Bamberg-Style Bock Rauchbier	0	0	0	0	0
Bamberg-Style Helles Rauchbier	0	0	0	0	0
Bamberg-Style Märzen Rauchbier	0	0	0	0	0
Bamberg-Style Weiss (Smoke) Rauchbier (Dunkel or Helles)	0	0	0	0	0
Barley Wine	0	0	0	0	0
Barrel-Aged	0	0	0	0	0
Belgian-style Fruit Beer	0	0	0	0	0
Belgian-Style Fruit Lambic	0	0	0	0	0
Belgian-Style Gueuze Lambic	0	0	0	0	0
Belgian-Style Lambic	0	0	0	0	0
Belgian-Style Quadrupel	0	0	0	0	0
Belgian-Style Table Beer	0	0	0	0	0
Bitter	0	0	0	0	0
Black	0	0	0	0	0
Blonde	1	142	1	0	16
Braggot	0	0	0	0	0
Brett Beer	0	0	0	0	0
Brown	0	0	0	0	0
California Common Beer	0	0	0	0	0
Chili Pepper Beer	0	0	0	0	0
Chocolate / Cocoa-Flavored Beer	0	0	0	0	0
Coffee-Flavored Beer	0	0	0	0	0
Common Cider	0	0	0	0	0
Common Perry	0	0	0	0	0
Contemporary Gose	0	0	0	0	0
Cyser (Apple Melomel)	0	0	0	0	0
Dark American-Belgo-Style Ale	0	0	0	0	0
Dortmunder / European-Style Export	0	0	0	0	0
Double India Pale Ale	0	0	0	0	0
Dry Mead	0	0	0	0	0
Dubbel	0	0	0	0	0
Dutch-Style Kuit, Kuyt or Koyt	0	0	0	0	0
Energy Enhanced Malt Beverage	0	0	0	0	0
English Cider	0	0	0	0	0
English-Style Dark Mild Ale	0	0	0	0	0
English-Style Pale Mild Ale	0	0	0	0	0
English-Style Summer Ale	0	0	0	0	0
European-Style Dark / Münchner Dunkel	0	0	0	0	0
Field Beer	0	0	0	0	0
Flavored Malt Beverage	0	0	0	0	0
French Cider	0	0	0	0	0
French-Style Bière de Garde	0	0	0	0	0
Fresh "Wet" Hop Ale	0	0	0	0	0
Fruit Beer	0	0	0	0	0
Fruit Cider	0	0	0	0	0
German-Style Doppelbock	0	0	0	0	0
German-Style Eisbock	0	0	0	0	0
German-Style Heller Bock/Maibock	0	0	0	0	0
German-Style Leichtbier	0	0	0	0	0
German-Style Leichtes Weizen / Weissbier	0	0	0	0	0
German-Style Märzen	0	0	0	0	0
German-Style Oktoberfest / Wiesen (Meadow)	0	0	0	0	0
German-Style Rye Ale (Roggenbier) with or without Yeast	0	0	0	0	0
German-Style Schwarzbier	0	0	0	0	0
Ginjo Beer or Sake-Yeast Beer	0	0	0	0	0
Gluten-Free Beer	0	0	0	0	0
Grodziskie	0	0	0	0	0
Herb and Spice Beer	0	0	0	0	0
Historical Beer	0	0	0	0	0
India Pale Ale	2	48	10	17	500
Kellerbier (Cellar beer) or Zwickelbier - Ale	0	0	0	0	0
Kölsch	0	0	0	0	0
Lager	0	0	0	0	0
Leipzig-Style Gose	0	0	0	0	0
Metheglin	0	0	0	0	0
Mixed Culture Brett Beer	0	0	0	0	0
Münchner (Munich)-Style Helles	0	0	0	0	0
New England Cider	0	0	0	0	0
Non-Alcoholic (Beer) Malt Beverages	0	0	0	0	0
Old Ale	0	0	0	0	0
Open Category Mead	0	0	0	0	0
Other Belgian-Style Ales	0	0	0	0	0
Other Fruit Melomel	0	0	0	0	0
Other Specialty Cider or Perry	0	0	0	0	0
Pale Ale	0	0	0	0	0
Pale American-Belgo-Style Ale	0	0	0	0	0
Pilsener	0	0	0	0	0
Porter	0	0	0	0	0
Pumpkin Beer	0	0	0	0	0
Pyment (Grape Melomel)	0	0	0	0	0
Red	0	0	0	0	0
Saison	0	0	0	0	0
Scotch Ale	0	0	0	0	0
Scottish-Style Export Ale	0	0	0	0	0
Scottish-Style Heavy Ale	0	0	0	0	0
Scottish-Style Light Ale	0	0	0	0	0
Semi-Sweet Mead	0	0	0	0	0
Session Beer	0	0	0	0	0
Sour	0	0	0	0	0
South German-Style Bernsteinfarbenes Weizen / Weissbier	0	0	0	0	0
South German-Style Dunkel Weizen / Dunkel Weissbier	0	0	0	0	0
South German-Style Kristall Weizen / Kristall Weissbier	0	0	0	0	0
South German-Style Weizenbock / Weissbock	0	0	0	0	0
Specialty Beer	0	0	0	0	0
Stout	58	6	135	0	4
Strong Ale	0	0	0	0	0
Sweet Mead	0	0	0	0	0
Traditional German-Style Bock	0	0	0	0	0
Traditional Perry	0	0	0	0	0
Tripel	3	3	1	0	58
Wheat	3	287	5	9	13
Wild Beer	0	0	0	0	0

Now that we have a manageable number of styles, we can see how well fit each cluster is to each style. If the features we clustered on perfectly predicted style, there would each color (cluster) would be unique to each facet of the plot. (E.g., left entirely blue, second from left entirely green, etc.)

by_style_plot <- ggplot() +   
  geom_point(data = certain_styles_clustered, 
             aes(x = abv, y = ibu,
                 colour = cluster_assignment), alpha = 0.5) +
  facet_grid(. ~ style_collapsed) +
  geom_point(data = style_centers_certain_styles,
           aes(mean_abv, mean_ibu), colour = "black", shape = 5) +
  ggtitle("Selected Styles Cluster Assignment") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster") +
  theme_bw()
by_style_plot

–>

Random asides into hops

Do more hops always mean more bitterness?

It would appear so, from this graph and this regression (beta = 2.394418)

ggplot(data = beer_ingredients_join, aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") + 
  ggtitle("Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

hops_ibu_lm <- lm(ibu ~ total_hops, data = beer_ingredients_join)
summary(hops_ibu_lm)


Call:
lm(formula = ibu ~ total_hops, data = beer_ingredients_join)

Residuals:
   Min     1Q Median     3Q    Max 
-39.95 -18.95  -7.25  14.92 959.05 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 40.95273    0.18040 227.008  < 2e-16 ***
total_hops   0.22822    0.06661   3.426 0.000613 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 26.97 on 23117 degrees of freedom
  (40376 observations deleted due to missingness)
Multiple R-squared:  0.0005076, Adjusted R-squared:  0.0004644 
F-statistic: 11.74 on 1 and 23117 DF,  p-value: 0.0006126

However, past a certain point (3 hops or more), there’s no effect of number of hops on IBU

ggplot(data = beer_ingredients_join[which(beer_ingredients_join$total_hops > 2
                                          & beer_ingredients_join$total_hops < 8), ], aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") +
  ggtitle("3+ Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

Most popular hops

# Gather up all the hops columns into one called `hop_name`
beer_necessities_hops_gathered <- beer_necessities %>%
  gather(
    hop_key, hop_name, hops_name_1:hops_name_13
  ) %>% as_tibble()
# Filter to just those beers that have at least one hop
beer_necessities_w_hops <- beer_necessities_hops_gathered %>% 
  filter(!is.na(hop_name)) %>% 
  filter(!hop_name == "")
beer_necessities_w_hops$hop_name <- factor(beer_necessities_w_hops$hop_name)
# For all hops, find the number of beers they're in as well as those beers' mean IBU and ABV
hops_beer_stats <- beer_necessities_w_hops %>% 
  ungroup() %>% 
  group_by(hop_name) %>% 
  summarise(
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_abv = mean(abv, na.rm = TRUE),
    n = n()
  )
# Pare to hops that are used in at least 50 beers
pop_hops_beer_stats <- hops_beer_stats[hops_beer_stats$n > 50, ]
kable(pop_hops_beer_stats)

hop_name	mean_ibu	mean_abv	n
Amarillo	61.36053	6.959264	163
Cascade	51.92405	6.510729	445
Centennial	63.96526	7.081883	243
Chinook	60.86871	7.043439	194
Citra	59.60000	6.733290	157
Columbus	63.74483	6.953846	183
East Kent Golding	38.51875	6.347386	89
Fuggles	40.75581	6.772143	59
Hallertauer (American)	23.92388	5.658537	83
Magnum	48.71596	6.926852	109
Mosaic	56.81818	6.977465	71
Mount Hood	37.83500	6.550000	68
Northern Brewer (American)	39.48475	6.473944	71
Nugget	52.23810	6.383119	114
Perle (American)	32.03947	6.251744	88
Saaz (American)	30.69778	6.248333	60
Simcoe	64.07211	6.877394	191
Sterling	35.41860	6.024259	55
Tettnanger (American)	30.27551	6.016780	59
Warrior	59.13043	6.983115	62
Willamette	39.61078	7.014657	133

# Keep just beers that contain these most popular hops
beer_necessities_w_popular_hops <- beer_necessities_w_hops %>% 
  filter(hop_name %in% pop_hops_beer_stats$hop_name) %>% 
  droplevels()

Are there certian hops that are used more often in very high IBU or ABV beers? Hard to detect a pattern

ggplot(data = beer_necessities_w_popular_hops) + 
  geom_point(aes(abv, ibu, colour = hop_name)) +
  ggtitle("Beers Containing most Popular Hops") +
  labs(x = "ABV", y = "IBU", colour = "Hop Name") +
  theme_minimal()

ggplot(data = pop_hops_beer_stats) + 
  geom_point(aes(mean_abv, mean_ibu, colour = hop_name, size = n)) +
  ggtitle("Most Popular Hops' Effect on Alcohol and Bitterness") +
  labs(x = "Mean ABV per Hop Type", y = "Mean IBU per Hop Type", colour = "Hop Name", 
       size = "Number of Beers") +
  theme_minimal()

Neural Net

Can ABV, IBU, and SRM be used in a neural net to predict style or style_collapsed?
In the function, specify the dataframe and the outcome, either style or style_collapsed; the one not specified as outcome will be dropped
The predictor columns will be everything not specified in the vector predictor_vars
The function returns the outcome variable sleected, neural net output, variable importance, the prediction dataframe, predictions, and accuracy

library(nnet)
library(caret)
run_neural_net <- function(df, outcome, predictor_vars) {
  out <- list(outcome = outcome)
  
  # Create a new column outcome; it's style_collapsed if you set outcome to style_collapsed, and style otherwise
  if (outcome == "style_collapsed") {
    df[["outcome"]] <- df[["style_collapsed"]]
  } else {
    df[["outcome"]] <- df[["style"]]
  }
  df$outcome <- factor(df$outcome)
  
  cols_to_keep <- c("outcome", predictor_vars)
  
  df <- df %>%
    select_(.dots = cols_to_keep) %>%
    mutate(row = 1:nrow(df)) %>% 
    droplevels()
  # Select 80% of the data for training
  df_train <- sample_n(df, nrow(df)*(0.8))
  
  # The rest is for testing
  df_test <- df %>%
    filter(! (row %in% df_train$row)) %>%
    select(-row)
  
  df_train <- df_train %>%
    select(-row)
  
  # Build multinomail neural net
  nn <- multinom(outcome ~ .,
                 data = df_train, maxit=500, trace=T)
  # Which variables are the most important in the neural net?
  most_important_vars <- varImp(nn)
  # How accurate is the model? Compare predictions to outcomes from test data
  nn_preds <- predict(nn, type="class", newdata = df_test)
  nn_accuracy <- postResample(df_test$outcome, nn_preds)
  out <- list(out, nn = nn, most_important_vars = most_important_vars,
              df_test = df_test,
              nn_preds = nn_preds,
           nn_accuracy = nn_accuracy)
  return(out)
}

Set the dataframe to be beer_totals, the predictor variables to be the vector contained in p_vars, the outcome to be style_collapsed

Take out NAs

bt_omit <- beer_totals %>% na.omit()

p_vars <- c("total_hops", "total_malt", "abv", "ibu", "srm")
nn_collapsed_out <- run_neural_net(df = bt_omit, outcome = "style_collapsed", 
                         predictor_vars = p_vars)

# weights:  266 (222 variable)
initial  value 800.268955 
iter  10 value 606.966534
iter  20 value 557.180737
iter  30 value 527.003811
iter  40 value 510.870829
iter  50 value 495.376651
iter  60 value 458.207968
iter  70 value 408.305952
iter  80 value 376.270666
iter  90 value 354.949715
iter 100 value 341.937012
iter 110 value 324.405452
iter 120 value 313.536578
iter 130 value 306.739580
iter 140 value 301.423593
iter 150 value 296.559338
iter 160 value 293.432943
iter 170 value 291.671564
iter 180 value 290.220037
iter 190 value 289.370752
iter 200 value 288.691856
iter 210 value 287.792355
iter 220 value 287.185759
iter 230 value 286.365962
iter 240 value 285.842047
iter 250 value 285.600407
iter 260 value 285.448644
iter 270 value 285.273483
iter 280 value 285.055191
iter 290 value 284.832262
iter 300 value 284.692212
iter 310 value 284.614784
iter 320 value 284.574410
iter 330 value 284.549547
iter 340 value 284.522034
iter 350 value 284.500604
iter 360 value 284.463509
iter 370 value 284.418475
iter 380 value 284.368603
iter 390 value 284.320421
iter 400 value 284.238956
iter 410 value 284.158280
iter 420 value 284.078921
iter 430 value 284.001264
iter 440 value 283.904806
iter 450 value 283.865220
iter 460 value 283.859244
iter 470 value 283.853966
iter 480 value 283.848464
iter 490 value 283.837598
iter 500 value 283.820386
final  value 283.820386 
stopped after 500 iterations

# How accurate was it?
nn_collapsed_out$nn_accuracy

 Accuracy     Kappa 
0.4000000 0.3452641

# What were the most important variables?
nn_collapsed_out$most_important_vars

What if we predcit style instead of style_collapsed?


nn_notcollapsed_out <- run_neural_net(df = bt_omit, outcome = "style", 
                         predictor_vars = p_vars)

nn_notcollapsed_out$nn_accuracy

nn_notcollapsed_out$most_important_vars

And now if we add glass as a predictor?


p_vars_add_glass <- c("total_hops", "total_malt", "abv", "ibu", "srm", "glass")

nn_collapsed_out_add_glass <- run_neural_net(df = beer_ingredients_join, outcome = "style_collapsed", 
                         predictor_vars = p_vars_no_glass)

nn_collapsed_out_add_glass$nn_accuracy

nn_collapsed_out_add_glass$most_important_vars

Random forest with all ingredients

We can use a random forest to get even more granular with ingredients
- The sparse ingredient dataframe was too complex for the multinomial neural net but the ranger package is built to handle sparse data like this
Here we don’t include glass as a predictor

library(ranger)
library(stringr)
bi <- beer_ingredients_join %>% 
  select(-c(id, name, style, hops_name, malt_name,
            # description,
            glass)) %>% 
  mutate(row = 1:nrow(.)) %>% 
  na.omit()
bi$style_collapsed <- factor(bi$style_collapsed)
# ranger complains about special characters and spaces in ingredient column names. Take them out and replace with empty string.
names(bi) <- tolower(names(bi))
names(bi) <- str_replace_all(names(bi), " ", "")
names(bi) <- str_replace_all(names(bi), "([\\(\\)-\\/')]+)", "")
# Keep 80% for training
bi_train <- sample_n(bi, nrow(bi)*(0.8))
# The rest is for testing
bi_test <- bi %>%
  filter(! (row %in% bi_train$row)) %>%
  dplyr::select(-row)
bi_train <- bi_train %>%
  dplyr::select(-row) %>% 
  select(-`#06300`)
bi_rf <- ranger(style_collapsed ~ ., data = bi_train, importance = "impurity", seed = 11)

OOB (out of bag) prediction error is around 58% * This calculated from tree samples constructed but not used in training set; these trees become effectively part of test set

bi_rf

We can compare predicted classification on the test set to their actual style classification.

pred_bi_rf <- predict(bi_rf, dat = bi_test)
table(bi_test$style_collapsed, pred_bi_rf$predictions)

Variable importance * Interestingly, ABV, IBU, and SRM are all much more important in the random forest than total_hops and total_malt


importance(bi_rf)[1:10]

How does a CSRF (case-specific random forest) fare?


bi_csrf <- csrf(style_collapsed ~ ., training_data = bi_train, test_data = bi_test,
                params1 = list(num.trees = 5, mtry = 4),
                params2 = list(num.trees = 2))

csrf_acc <- postResample(bi_csrf, bi_test$style_collapsed)

csrf_acc

Final Thoughts

Style first, forgiveness later?

One reason seems that beers are generally brewed with style in mind first (“let’s make a pale ale”) rather than deciding the beer’s style after determining its characteristics and idiosyncrasies
- Even if the beer turns out more like a sour, and in a blind taste test might be classified as a sour more often than a pale ale, it still gets the label pale ale
- This makes the style definitions broader and harder to predict

Future Directions

Incorporate flavor profiles for beers sourced/scraped from somewhere
Implement a GAN to come up with beer names
More on the hops deep dive: which hops are used most often in which styles?

---
title: Data Science Musings on Beer
author:
  name: Amanda Dobbyn
date: '`r format(Sys.time(), "%B %d, %Y")`'
# output:
#   html_notebook:
#     toc: false
#     theme: yeti
#   pdf_document:
#     keep_tex: true
#     toc: false
#   github_document:
#     toc: true
    
output:
  html_document:
    keep_md: true
    toc: false
    theme: yeti
  github_document:
    toc: true
---

```{r, eval=FALSE}
# If need to close all connections
lapply( dbListConnections( dbDriver( drv = "MySQL")), dbDisconnect)
```

```{r setup, include=FALSE}
library(knitr)

# knitr::opts_knit$set(root.dir=normalizePath('../'))
knitr::opts_chunk$set(echo = FALSE, warning = FALSE)
knitr::opts_chunk$set(fig.width=12, fig.height=8) 
options(knitr.table.format = 'markdown')

# source("./read_from_db.R")
source("./most_popular_styles.R")
# # source("./cluster.R")
# # source("./plot.R")
# source("./get_ingredient_levels.R")
```

This is a first pass exploration of different aspects of beer.

* Data courtesy of [BreweryDB](http://www.brewerydb.com/developers)
    * Special thanks to [Kris Kroski](https://kro.ski/) for data ideation and beer
    
    
*** 


* The main question on the table is this:
    * Are beer styles actually indicative of shared attributes of the beers within that style? Or are style boundaries more or less arbitrary?
      * Two approaches: clustering and prediction 
      * Clustering: are there natural clusters across the spectum of beers that align well with the styles they're grouped into? 
          * Unsupervised (k-means) clustering based on 
              * ABV (alcohol by volume), IBU (international bitterness units), SRM (measure of color)
              * How well do these match up with various "style centers," defined by mean of ABV, IBU, and SRM per beer style
      * Prediction: can we predict a beer's style based on certain characteristics of the beer?
          * Neural net 
          * Random forest
      
* Answer thus far
    * Beer-intrinsic attributes aren't great predictors of style
    * Style-defined attributes are the best predictors
        * For instance, the glass a beer is served in (which is defined by its style) is a much better predictor of its style than actual characteristics of the beer like ABV and even the number of different types of hops it contains

![](./taps.jpg)



### Workflow Overview

* Hit the BreweryDB API to iteratively pull in all beers and their ingredients along with other things we might want like breweries and glassware
* Unnest the JSON responses, including all the ingredients columns, and 
* Dump this all into a MySQL database 

* Create a `style_collapsed` column to reduce the number of levels of our outcome variable
    * `grep` through each beer's style to determine if that style contains a keyword that qualifies it to be rolled into a collapsed style
    * If it does, it gets that keyword in a `style_collapsed` column 
    * Further collpase styles that are similar like Hefeweizen and Wit into Wheat
    
* Unnest the ingredients `hops` and `malts` into a sparse matrix
    * Individual ingredients as columns, beers as rows; cell gets a 1 if ingredient is present and 0 otherwise 
    
* Cluster: unsupervised k-means clsutering based on ABV, IBU, and SRM

* Run a neural net
    * Predict either `style` or `style_collapsed` from all the predictors including the total number of hops and malts per beer


**Short Aside**

The question of what should be a predictor variable for style is a bit murky here. What should be fair game for predicting style and what shouldn't? Characteristics of a beer that are defined *by* its style would seem to be "cheating" in a way. 

* Main candidates are:
    * ABV (alcohol by volume), IBU (international bitterness units), SRM (standard reference measure, a scale of beer color from light to dark)
        * These are outputs of a beer that meaningfully define the beer and are theoretically orthogonal to each other
    * Ingredients in a beer such as hops and malts
        * Inputs to a beer that have some effect on its flavor profile
        * Semi-cheating because if style is determined beforehand it likely determines at least in part which ingredients are added 
    * Glass type
        * This is defined entirely by style and is very predictive of it



**This document compiled by querying the beer database I built, specifically by sourcing the file read_from_db.R. This is done for expediency's sake, (the code below detailing how to get the beer, run in full in run_it.R, takes some time to execute).** 


### Get and Prepare Data

**Getting beer, the age-old dilemma**

* The BreweryDB API returns a certain number of results per page; if we want 
* So, we hit the BreweryDB API and ask for `1:number_of_pages`
    * We can change `number_of_pages` to, e.g., 3 if we only want the first 3 pages
    * If there's only one page (as is the case for the glassware endpoing), numberOfPages won't be returned, so in this case we set number_of_pages to 1
* The `addition` parameter can be an empty string if nothing else is needed

```{r, eval = FALSE, echo=TRUE}

base_url <- "http://api.brewerydb.com/v2"
key_preface <- "/?key="

paginated_request <- function(ep, addition) {    
  full_request <- NULL
  first_page <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                , "&p=1"))
  number_of_pages <- ifelse(!(is.null(first_page$numberOfPages)), 
                            first_page$numberOfPages, 1)      

    for (page in 1:number_of_pages) {                               
    this_request <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                    , "&p=", page, addition),
                             flatten = TRUE) 
    this_req_unnested <- unnest_it(this_request)    #  <- request unnested here
    print(this_req_unnested$currentPage)
    full_request <- bind_rows(full_request, this_req_unnested[["data"]])
  }
  full_request
} 

all_beer_raw <- paginated_request("beers", "&withIngredients=Y")
```



* Function for unnesting JSON used inside `paginated_request()` below
    + Takes the column named `name` nested within a column in the data portion of the response
        + If the `name` column doesn't exist, it takes the first nested column
* We use something similar to unnest ingredient like all of a beer's hops and malts into a long string contained in `hops_name` and `malt_name`

```{r, eval=FALSE, echo=TRUE}
unnest_it <- function(df) {
  unnested <- df
  for(col in seq_along(df[["data"]])) {
    if(! is.null(ncol(df[["data"]][[col]]))) {
      if(! is.null(df[["data"]][[col]][["name"]])) {
        unnested[["data"]][[col]] <- df[["data"]][[col]][["name"]]
      } else {
        unnested[["data"]][[col]] <- df[["data"]][[col]][[1]]
      }
    }
  }
  unnested
}
```



**Collapse Styles**

* Save the most popular styles in `keywords`
* Loop through each keyword
    * For each beer, `grep` through its style column to see if it contains any one of these keywords
    * If it does, give it that keyword in a new column `style_collapsed`
* If a beer's name matches multiple keywords, e.g., American Double India Pale Ale would match Double India Pale Ale, India Pale Ale, and Pale Ale, its `style_collapsed` is the **last** of those that appear in keywords 
    * This is why keywords are intentionally ordered from most general to most specific
    * So in the case of an case of American Double India Pale Ale: since Double India Pale Ale appears in `keywords` after India Pale Ale and Pale Ale, an American Double India Pale Ale would get a `style_collapsed` of Double India Pale Ale
* If no keyword is contained in `style`, `style_collapsed` is just whatever's in `style`; in other words, it doesn't get collpsed into a bigger bucket
    * This isn't a huge problem because we'll pare down to just the most popular styles later, however we could think about creating a catchall "Other" level for `style_collapsed`

```{r, eval=FALSE, echo=TRUE}

collapse_styles <- function(df) {
  keywords <- c("Lager", "Pale Ale", "India Pale Ale", "Double India Pale Ale", "India Pale Lager", "Hefeweizen", "Barrel-Aged","Wheat", "Pilsner", "Pilsener", "Amber", "Golden", "Blonde", "Brown", "Black", "Stout", "Porter", "Red", "Sour", "Kölsch", "Tripel", "Bitter", "Saison", "Strong Ale", "Barley Wine", "Dubbel", "Altbier")
  
  for (beer in 1:nrow(df)) {
    if (grepl(paste(keywords, collapse="|"), df$style[beer])) {    
      for (keyword in keywords) {         
        if(grepl(keyword, df$style[beer]) == TRUE) {
          df$style_collapsed[beer] <- keyword    
        }                         
      } 
    } else {
      df$style_collapsed[beer] <- as.character(df$style[beer])       
    }
    print(df$style_collapsed[beer])
  }
  return(df)
}

```

* Then we collapse further; right now we just combine all wheaty bears into Wheat and Pils-like beers into Pilsener (with two e's) by `fct_collapse`ing those levels

```{r, echo=TRUE, eval=FALSE}
collapse_further <- function(df) {
  df[["style_collapsed"]] <- df[["style_collapsed"]] %>%
    fct_collapse(
      "Wheat" = c("Hefeweizen", "Wheat"),
      "Pilsener" = c("Pilsner", "American-Style Pilsener") # pilsener == pilsner == pils
    )
  return(df)
}
```



**Split out Ingredients**

* When we unnested ingredients, we just concatenated all of the ingredients for a given beer into a long string
* If we want, we can split out the ingredients that were concatenated in `<ingredient>_name` with this `split_ingredients` function
* This takes a vector of `ingredients_to_split`, so e.g. `c("hops_name", "malt_name")` and creates one column for each type of ingredient (`hops_name_1`, `hops_name_2`, etc.)

* We `str_split` on the ingredient and get a list back
* We find the max number of instances of an ingredient per beer, which will be the number of columns we're adding
* For each new column we need, we create it, initialize it with NAs, and name it
* Then for each element in our list of split up ingredients, if it exists, we add it to the correct column in our df

```{r, eval=FALSE, echo=TRUE}
split_ingredients <- function(df, ingredients_to_split) {
  
  ncol_df <- ncol(df)
  
  for (ingredient in ingredients_to_split) {

    ingredient_split <- str_split(df[[ingredient]], ", ")    
    num_new_cols <- max(lengths(ingredient_split))    
  
    for (num in 1:num_new_cols) {
      
      this_col <- ncol_df + 1         
      
      df[, this_col] <- NA
      names(df)[this_col] <- paste0(ingredient, "_", num)
      ncol_df <- ncol(df)             
      for (row in seq_along(ingredient_split)) {          
        if (!is.null(ingredient_split[[row]][num])) {        
          df[row, this_col] <- ingredient_split[[row]][num]
        }
      }
      df[[names(df)[this_col]]] <- factor(df[[names(df)[this_col]]])
    }
    
    ncol_df <- ncol(df)
  }
  return(df)
}
```



**Find the Most Popualar Styles**

* Find mean ABV, IBU, and SRM per collapsed style
* Arrange collapsed styles by the number of beers that fall into them
    * This is of course dependent on how we collapse styles

```{r, eval=FALSE, echo=TRUE}
library(forcats)

# Pare down to only cases where style is not NA
beer_dat <- beer_necessities

beer_dat_pared <- beer_dat[complete.cases(beer_dat$style), ]

# Arrange beer dat by style popularity
style_popularity <- beer_dat_pared %>% 
  group_by(style) %>% 
  count() %>% 
  arrange(desc(n))
style_popularity

# Add a column that scales popularity
style_popularity <- bind_cols(style_popularity, 
                               n_scaled = as.vector(scale(style_popularity$n)))

# Find styles that are above a z-score of 0
popular_styles <- style_popularity %>% 
  filter(n_scaled > 0)

# Pare dat down to only beers that fall into those styles
popular_beer_dat <- beer_dat_pared %>% 
  filter(
    style %in% popular_styles$style
  ) %>% 
  droplevels() %>% 
  as_tibble() 
nrow(popular_beer_dat)

# Find the centers (mean abv, ibu, srm) of the most popular styles
style_centers <- popular_beer_dat %>% 
  group_by(style_collapsed) %>% 
  add_count() %>% 
  summarise(
    mean_abv = mean(abv, na.rm = TRUE),
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_srm = mean(srm, na.rm = TRUE),
    n = median(n, na.rm = TRUE)          # Median here only for summarise. Should be just the same as n
  ) %>% 
  arrange(desc(n)) %>% 
  drop_na() %>% 
  droplevels()

# Give some nicer names
style_centers_rename <- style_centers %>% 
  rename(
    `Collapsed Style` = style_collapsed,
    `Mean ABV` = mean_abv,
    `Mean IBU` = mean_ibu,
    `Mean SRM` = mean_srm,
    `Numer of Beers` = n
  )
```


Take a look at the table      

```{r}
kable(style_centers_rename)
```


***

Now that the munging is done, onto the main question: do natural clusters in beer align with style boundaries?




***

### Ingredients

To get more granular with ingredients, we can split out each individual ingredient into its own column. If a beer or style contains that ingredient, its row gets a 1 in that ingredient column and a 0 otherwise.

From this, we can find the total number of hops and malts per grouper.

* The dataframe we'll use will be `beer_necessities`


<!-- ```{r, eval=TRUE, echo=TRUE} -->
<!-- clustered_beer_necessities <- clustered_beer %>% -->
<!--   inner_join(beer_necessities) -->

<!-- ``` -->

* This function takes a dataframe and two other parameters set at the outset:
    * `ingredient_want`: this can be `hops`, `malt`, or other ingredients like `yeast` if we pull that in
    * `grouper`: can be a vector of one or more things to group by, like beer `name` or `style`

```{r, eval=TRUE, echo=TRUE}

pick_ingredient_get_beer <- function (ingredient_want, df, grouper) {
  
  # ----------------------- Setup --------------------------- #
  # We've already split ingredient number names out from the concatenated string into columns like `malt_name_1`,
  # `malt_name_2`, etc. We need to find the range of these columns; there will be a different number of malt
  # columns than hops columns, for instance. The first one will be `<ingredient>_name_1` and from this we can find
  # the index of this column in our dataframe. We get the name of last one with the `get_last_ing_name_col()`
  # function. Then we save a vector of all the ingredient column names in `ingredient_colnames`. It will stay
  # constant even if the indices change when we select out certain columns. 
  
  # First ingredient
  first_ingredient_name <- paste(ingredient_want, "_name_1", sep="")
  first_ingredient_index <- which(colnames(df)==first_ingredient_name)
  
  # Get the last ingredient
  get_last_ing_name_col <- function(df) {
    for (col in names(df)) {
      if (grepl(paste(ingredient_want, "_name_", sep = ""), col) == TRUE) {
        name_last_ing_col <- col
      }
    }
    return(name_last_ing_col)
  }
  
  # Last ingredient
  last_ingredient_name <- get_last_ing_name_col(df)
  last_ingredient_index <- which(colnames(df)==last_ingredient_name)
  
  # Vector of all the ingredient column names
  ingredient_colnames <- names(df)[first_ingredient_index:last_ingredient_index]
  
  # Non-ingredient column names we want to keep
  to_keep_col_names <- c("cluster_assignment", "name", "abv", "ibu", "srm", "style", "style_collapsed")
  
  # -------------------------------------------------------------------------------# 
  
  # Inside `gather_ingredients()` we take out superflous column names that are not in `to_keep_col_names` or one 
  # of the ingredient columns, find what the new ingredient column indices are, since they'll have changed after 
  # we pared down and then gather all of the ingredient columns (e.g., `hops_name_1`) into one long column, 
  # `ing_keys` and all the actual ingredient names (e.g., Cascade) into `ing_names`.
  
  # ----------------------------- Gather columns --------------------------------- #
  gather_ingredients <- function(df, cols_to_gather) {
    to_keep_indices <- which(colnames(df) %in% to_keep_col_names)
    
    selected_df <- df[, c(to_keep_indices, first_ingredient_index:last_ingredient_index)]
    
    new_ing_indices <- which(colnames(selected_df) %in% cols_to_gather)    # indices will have changed since we pared down 
    
    df_gathered <- selected_df %>%
      gather_(
        key_col = "ing_keys",
        value_col = "ing_names",
        gather_cols = colnames(selected_df)[new_ing_indices]
      ) %>%
      mutate(
        count = 1
      )
    df_gathered
  }
  beer_gathered <- gather_ingredients(df, ingredient_colnames)  # ingredient colnames defined above function
  # ------------------------------------------------------------------------------- # 
  
  # Next we get a vector of all ingredient levels and take out the one that's an empty string and 
  # use this vector of ingredient levels in `select_spread_cols()` below

  # Get a vector of all ingredient levels
  beer_gathered$ing_names <- factor(beer_gathered$ing_names)
  ingredient_levels <- levels(beer_gathered$ing_names) 
  
  # Take out the level that's just an empty string
  to_keep_levels <- !(c(1:length(ingredient_levels)) %in% which(ingredient_levels == ""))
  ingredient_levels <- ingredient_levels[to_keep_levels]
  
  beer_gathered$ing_names <- as.character(beer_gathered$ing_names)
  
  # ----------------------------------------------------------------------------- # 
  
  # Then we spread the ingredient names: we take what was previously the `value` in our gathered dataframe, the
  # actual ingredient names (Cascade, Centennial) and make that our `key`; it'll form the new column names. The
  # new `value` is `value` is count; it'll populate the row cells. If a given row has a certain ingredient, it
  # gets a 1 in the corresponding cell, an NA otherwise. 
  # We add a unique idenfitier for each row with `row`, which we'll drop later (see [Hadley's SO
  # comment](https://stackoverflow.com/questions/25960394/unexpected-behavior-with-tidyr)).

  
  # ------------------------------- Spread columns -------------------------------- #
  spread_ingredients <- function(df) {
    df_spread <- df %>% 
      mutate(
        row = 1:nrow(df)        # Add a unique idenfitier for each row which we'll need in order to spread; we'll drop this later
      ) %>%                                 
      spread(
        key = ing_names,
        value = count
      ) 
    return(df_spread)
  }
  beer_spread <- spread_ingredients(beer_gathered)
  # ------------------------------------------------------------------------------- # 

  
  # ------------------------- Select only certain columns ------------------------- #
  select_spread_cols <- function(df) {
    to_keep_col_indices <- which(colnames(df) %in% to_keep_col_names)
    to_keep_ingredient_indices <- which(colnames(df) %in% ingredient_levels)
    
    to_keep_inds_all <- c(to_keep_col_indices, to_keep_ingredient_indices)
    
    new_df <- df %>% 
      select_(
        .dots = to_keep_inds_all
      )
    return(new_df)
  }
  beer_spread_selected <- select_spread_cols(beer_spread)
  # ------------------------------------------------------------------------------- # 

  # Take out all rows that have no ingredients specified at all
  inds_to_remove <- apply(beer_spread_selected[, first_ingredient_index:last_ingredient_index], 
                          1, function(x) all(is.na(x)))
  beer_spread_no_na <- beer_spread_selected[ !inds_to_remove, ]
  
  
  # ----------------- Group ingredients by the grouper specified ------------------- #
  # Then we do the final step and group by the groupers.
  
  get_ingredients_per_grouper <- function(df, grouper = grouper) {
    df_grouped <- df %>%
      ungroup() %>% 
      group_by_(grouper)
    
    not_for_summing <- which(colnames(df_grouped) %in% to_keep_col_names)
    max_not_for_summing <- max(not_for_summing)
    
    per_grouper <- df_grouped %>% 
      select(-c(abv, ibu, srm)) %>%    # taking out temporarily
      summarise_if(
        is.numeric,              
        sum, na.rm = TRUE
        # -c(abv, ibu, srm)
      ) %>%
      mutate(
        total = rowSums(.[(max_not_for_summing + 1):ncol(.)], na.rm = TRUE)    
      )
    
    # Send total to the second position
    per_grouper <- per_grouper %>% 
      select(
        name, total, everything()
      )
    
    # Replace total column with more descriptive name: total_<ingredient>
    names(per_grouper)[which(names(per_grouper) == "total")] <- paste0("total_", ingredient_want)
    
    return(per_grouper)
  }
  # ------------------------------------------------------------------------------- # 
  
  ingredients_per_grouper <- get_ingredients_per_grouper(beer_spread_selected, grouper)
  return(ingredients_per_grouper)
}
```


* Now run the function with `ingredient_want` as first hops, then malt
* Then join the resulting dataframes and remove/reorder some columns

```{r, echo=TRUE, eval=TRUE}
# Run the entire function with ingredient_want set to hops, grouping by name
ingredients_per_beer_hops <- pick_ingredient_get_beer(ingredient_want = "hops", 
                                                      beer_necessities, 
                                                      grouper = c("name", "style_collapsed"))

# Same for malt
ingredients_per_beer_malt <- pick_ingredient_get_beer(ingredient_want = "malt", 
                                                      beer_necessities, 
                                                      grouper = c("name", "style_collapsed"))

# Join those on our original dataframe by name
beer_ingredients_join_first_ingredient <- left_join(beer_necessities, ingredients_per_beer_hops,
                                                    by = "name")
beer_ingredients_join <- left_join(beer_ingredients_join_first_ingredient, ingredients_per_beer_malt,
                                   by = "name")


# Take out some unnecessary columns
unnecessary_cols <- c("styleId", "abv_scaled", "ibu_scaled", "srm_scaled", 
                      "hops_id", "malt_id", "glasswareId", "style.categoryId")
beer_ingredients_join <- beer_ingredients_join[, (! names(beer_ingredients_join) %in% unnecessary_cols)]


# If we also want to take out any of the malt_name_1, malt_name_2, etc. columns we can do this with a grep
more_unnecessary <- c("hops_name_|malt_name_")
beer_ingredients_join <- 
  beer_ingredients_join[, (! grepl(more_unnecessary, names(beer_ingredients_join)) == TRUE)]

# Reorder columns a bit
beer_ingredients_join <- beer_ingredients_join %>% 
  select(
    id, name, total_hops, total_malt, everything(), -description
  )

# And get a df that includes total_hops and total_malt but not all the other ingredient columns
beer_totals <- beer_ingredients_join %>% 
  select(
    id, name, total_hops, total_malt, style, style_collapsed,
    abv, ibu, srm, glass, hops_name, malt_name
  )

```



Now we're left with something of a sparse matrix of all the ingredients compared to all the beers
```{r}
kable(beer_ingredients_join[1:20, ])
```




***

### Unsupervised Clustering 
We K-means cluster beers based on certain numeric predictor variables. 


**Prep**

* Write a funciton that takes a dataframe, a set of predictors, a response variable, and the number of cluster centers you want
    * NB: There are not not very many beers have SRM so we may not want to omit based on it

* Take out missing values, and scale the data
* Take out outliers, defined as beers have to have an ABV between 3 and 20 and an IBU less than 200
* Then cluster on just the predictors and compare to the response variable
  

```{r, echo=TRUE}

library(NbClust)

cluster_it <- function(df, preds, to_scale, resp, n_centers) {
  df_for_clustering <- df %>%
    select_(.dots = c(response_vars, cluster_on)) %>%
    na.omit() %>%
    filter(
      abv < 20 & abv > 3
    ) %>%
    filter(
      ibu < 200
    )

  df_all_preds <- df_for_clustering %>%
    select_(.dots = preds)

  df_preds_scale <- df_all_preds %>%
    select_(.dots = to_scale) %>%
    rename(
      abv_scaled = abv,
      ibu_scaled = ibu,
      srm_scaled = srm
    ) %>%
    scale() %>%
    as_tibble()

  df_preds <- bind_cols(df_preds_scale, df_all_preds[, (!names(df_all_preds) %in% to_scale)])

  df_outcome <- df_for_clustering %>%
    select_(.dots = resp) %>%
    na.omit()

  set.seed(9)
  clustered_df_out <- kmeans(x = df_preds, centers = n_centers, trace = TRUE)

  clustered_df <- as_tibble(data.frame(
    cluster_assignment = factor(clustered_df_out$cluster),
    df_outcome, df_preds,
    df_for_clustering %>% select(abv, ibu, srm)))

  return(clustered_df)
}

```



 
**Cluster**

First we'll run the fuction with 10 centers, and cluster on the predictors ABV, IBU, SRM, total_hops, and total_malt.


```{r, echo=TRUE}

cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")

clustered_beer <- cluster_it(df = beer_totals,
                             preds = cluster_on,
                             to_scale = to_scale,
                             resp = response_vars,
                             n_centers = 10)
```


Head of the clustering data
```{r}
kable(clustered_beer[1:20, ])
```

Join the clustered beer on `beer_ingredients_join`
```{r}
beer_ingredients_join_clustered <- left_join(beer_ingredients_join, clustered_beer, 
                                             by = "name")
```


A table of cluster counts broken down by style
```{r}
cluster_table_counts <- table(style = clustered_beer$style_collapsed, cluster = clustered_beer$cluster_assignment)

kable(cluster_table_counts)
```


Plot the clusters. There are 3 axes: ABV, IBU, and SRM, so we choose two at a time. 

```{r, echo=TRUE}
clustered_beer_plot_abv_ibu <- ggplot(data = clustered_beer, aes(x = abv, y = ibu, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_ibu

clustered_beer_plot_abv_srm <- ggplot(data = clustered_beer, aes(x = abv, y = srm, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "SRM") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_srm
```



Now we can add in the style centers (means) for each `style_collapsed` and label it.

```{r, echo=TRUE}
library(ggrepel)
abv_ibu_clusters_vs_style_centers <- ggplot() +   
  geom_point(data = clustered_beer, 
             aes(x = abv, y = ibu, colour = cluster_assignment), alpha = 0.5) +
  geom_point(data = style_centers,
             aes(mean_abv, mean_ibu), colour = "black") +
  geom_text_repel(data = style_centers, aes(mean_abv, mean_ibu, label = style_collapsed), 
                  box.padding = unit(0.45, "lines"),
                  family = "Calibri",
                  label.size = 0.3) +
  ggtitle("Popular Styles vs. k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment") +
  theme_bw()
abv_ibu_clusters_vs_style_centers
```


The clustering above used a smaller number of clusters (10) than there are `styles_collapsed`. That makes it difficult to determine whether a given style fits snugly into a cluster or not.



**Cluster on just certain selected styles**

We'll take five very distinct collapsed styles and re-run the clustering on beers that fall into these categories. 
These styles were intentionally chosen because they are quite distinct: Blonde, IPA, Stout, Tripel, Wheat. Arguably, of these five styles Blondes and Wheats are the closest



```{r, echo=TRUE}
styles_to_keep <- c("Blonde", "India Pale Ale", "Stout", "Tripel", "Wheat")
bt_certain_styles <- beer_totals %>%
  filter(
    style_collapsed %in% styles_to_keep
  )


cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")

certain_styles_clustered <- cluster_it(df = bt_certain_styles,
                                 preds = cluster_on,
                                 to_scale = to_scale,
                                 resp = response_vars,
                                 n_centers = 5)

style_centers_certain_styles <- style_centers %>% 
  filter(style_collapsed %in% styles_to_keep)
```





Table of style vs. cluster.
```{r}
kable(table(style = certain_styles_clustered$style_collapsed, cluster = certain_styles_clustered$cluster_assignment))
```



Now that we have a manageable number of styles, we can see how well fit each cluster is to each style. If the features we clustered on perfectly predicted style, there would each color (cluster) would be unique to each facet of the plot. (E.g., left entirely blue, second from left entirely green, etc.)



```{r, echo=TRUE}
by_style_plot <- ggplot() +   
  geom_point(data = certain_styles_clustered, 
             aes(x = abv, y = ibu,
                 colour = cluster_assignment), alpha = 0.5) +
  facet_grid(. ~ style_collapsed) +
  geom_point(data = style_centers_certain_styles,
           aes(mean_abv, mean_ibu), colour = "black", shape = 5) +
  ggtitle("Selected Styles Cluster Assignment") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster") +
  theme_bw()
by_style_plot
```




<!-- ### Back to clustering: cluster on only 5 styles -->

<!-- * We'll pare down the beer data to just beers in 5 selected styles; 
<!-- * We'll cluster these into 5 clusters -->
<!-- <!-- * This time we'll add in `total_hops` and `total_malt` as predictors  --> -->




<!-- ggplot() + -->
<!--   geom_point(data = certain_styles_clustered, -->
<!--              aes(x = abv, y = ibu, -->
<!--                  shape = cluster_assignment, -->
<!--                  colour = style_collapsed), alpha = 0.5) + -->
<!--   geom_point(data = style_centers_certain_styles, -->
<!--              aes(mean_abv, mean_ibu), colour = "black") + -->
<!--   geom_text_repel(data = style_centers_certain_styles, -->
<!--                   aes(mean_abv, mean_ibu, label = style_collapsed), -->
<!--                   box.padding = unit(0.45, "lines"), -->
<!--                   family = "Calibri", -->
<!--                   label.size = 0.3) + -->
<!--   ggtitle("Selected Styles (colors) matched with Cluster Assignments (shapes)") + -->
<!--   labs(x = "ABV", y = "IBU") + -->
<!--   labs(colour = "Style", shape = "Cluster Assignment") + -->
<!--   theme_bw() -->

<!-- ``` -->



## Random asides into hops

**Do more hops always mean more bitterness?**

* It would appear so, from this graph and this regression (beta = 2.394418)
```{r, echo=TRUE}

ggplot(data = beer_ingredients_join, aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") + 
  ggtitle("Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

hops_ibu_lm <- lm(ibu ~ total_hops, data = beer_ingredients_join)
summary(hops_ibu_lm)
```

* However, past a certain point (3 hops or more), there's no effect of number of hops on IBU
```{r, echo=TRUE}
ggplot(data = beer_ingredients_join[which(beer_ingredients_join$total_hops > 2
                                          & beer_ingredients_join$total_hops < 8), ], aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") +
  ggtitle("3+ Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()
```


**Most popular hops**

```{r, echo=TRUE}
# Gather up all the hops columns into one called `hop_name`
beer_necessities_hops_gathered <- beer_necessities %>%
  gather(
    hop_key, hop_name, hops_name_1:hops_name_13
  ) %>% as_tibble()

# Filter to just those beers that have at least one hop
beer_necessities_w_hops <- beer_necessities_hops_gathered %>% 
  filter(!is.na(hop_name)) %>% 
  filter(!hop_name == "")

beer_necessities_w_hops$hop_name <- factor(beer_necessities_w_hops$hop_name)

# For all hops, find the number of beers they're in as well as those beers' mean IBU and ABV
hops_beer_stats <- beer_necessities_w_hops %>% 
  ungroup() %>% 
  group_by(hop_name) %>% 
  summarise(
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_abv = mean(abv, na.rm = TRUE),
    n = n()
  )

# Pare to hops that are used in at least 50 beers
pop_hops_beer_stats <- hops_beer_stats[hops_beer_stats$n > 50, ]
kable(pop_hops_beer_stats)

# Keep just beers that contain these most popular hops
beer_necessities_w_popular_hops <- beer_necessities_w_hops %>% 
  filter(hop_name %in% pop_hops_beer_stats$hop_name) %>% 
  droplevels() 
```

Are there certian hops that are used more often in very high IBU or ABV beers?
Hard to detect a pattern
```{r, echo = TRUE}
ggplot(data = beer_necessities_w_popular_hops) + 
  geom_point(aes(abv, ibu, colour = hop_name)) +
  ggtitle("Beers Containing most Popular Hops") +
  labs(x = "ABV", y = "IBU", colour = "Hop Name") +
  theme_minimal()
```

```{r, echo=TRUE}
ggplot(data = pop_hops_beer_stats) + 
  geom_point(aes(mean_abv, mean_ibu, colour = hop_name, size = n)) +
  ggtitle("Most Popular Hops' Effect on Alcohol and Bitterness") +
  labs(x = "Mean ABV per Hop Type", y = "Mean IBU per Hop Type", colour = "Hop Name", 
       size = "Number of Beers") +
  theme_minimal()
```


# Neural Net

* Can ABV, IBU, and SRM be used in a neural net to predict `style` or `style_collapsed`?
* In the function, specify the dataframe and the outcome, either `style` or `style_collapsed`; the one not specified as `outcome` will be dropped
* The predictor columns will be everything not specified in the vector `predictor_vars`
* The function returns the outcome variable sleected, neural net output, variable importance, the prediction dataframe, predictions, and accuracy

```{r, warning=FALSE, echo=TRUE, eval=TRUE, message=FALSE}

library(nnet)
library(caret)

run_neural_net <- function(df, outcome, predictor_vars) {
  out <- list(outcome = outcome)
  
  # Create a new column outcome; it's style_collapsed if you set outcome to style_collapsed, and style otherwise
  if (outcome == "style_collapsed") {
    df[["outcome"]] <- df[["style_collapsed"]]
  } else {
    df[["outcome"]] <- df[["style"]]
  }

  df$outcome <- factor(df$outcome)
  
  cols_to_keep <- c("outcome", predictor_vars)
  
  df <- df %>%
    select_(.dots = cols_to_keep) %>%
    mutate(row = 1:nrow(df)) %>% 
    droplevels()

  # Select 80% of the data for training
  df_train <- sample_n(df, nrow(df)*(0.8))
  
  # The rest is for testing
  df_test <- df %>%
    filter(! (row %in% df_train$row)) %>%
    select(-row)
  
  df_train <- df_train %>%
    select(-row)
  
  # Build multinomail neural net
  nn <- multinom(outcome ~ .,
                 data = df_train, maxit=500, trace=T)

  # Which variables are the most important in the neural net?
  most_important_vars <- varImp(nn)

  # How accurate is the model? Compare predictions to outcomes from test data
  nn_preds <- predict(nn, type="class", newdata = df_test)
  nn_accuracy <- postResample(df_test$outcome, nn_preds)

  out <- list(out, nn = nn, most_important_vars = most_important_vars,
              df_test = df_test,
              nn_preds = nn_preds,
           nn_accuracy = nn_accuracy)

  return(out)
}

```

* Set the dataframe to be `beer_totals`, the predictor variables to be the vector contained in `p_vars`, the outcome to be `style_collapsed`


Take out NAs
```{r}
bt_omit <- beer_totals %>% na.omit()
```

```{r, echo=TRUE, eval=TRUE, error=TRUE}
p_vars <- c("total_hops", "total_malt", "abv", "ibu", "srm")

nn_collapsed_out <- run_neural_net(df = bt_omit, outcome = "style_collapsed", 
                         predictor_vars = p_vars)


# How accurate was it?
nn_collapsed_out$nn_accuracy

# What were the most important variables?
nn_collapsed_out$most_important_vars

```


* What if we predcit `style` instead of `style_collapsed`?

```{r, echo=TRUE, error=TRUE}

nn_notcollapsed_out <- run_neural_net(df = bt_omit, outcome = "style", 
                         predictor_vars = p_vars)

nn_notcollapsed_out$nn_accuracy

nn_notcollapsed_out$most_important_vars

```


And now if we add `glass` as a predictor?
```{r, echo=TRUE, error=TRUE}

p_vars_add_glass <- c("total_hops", "total_malt", "abv", "ibu", "srm", "glass")

nn_collapsed_out_add_glass <- run_neural_net(df = beer_ingredients_join, outcome = "style_collapsed", 
                         predictor_vars = p_vars_no_glass)

nn_collapsed_out_add_glass$nn_accuracy

nn_collapsed_out_add_glass$most_important_vars

```




### Random forest with all ingredients

* We can use a random forest to get even more granular with ingredients
    * The sparse ingredient dataframe was too complex for the multinomial neural net but the `ranger` package is built to handle sparse data like this

* Here we don't include `glass` as a predictor

```{r, echo=TRUE}

library(ranger)
library(stringr)

bi <- beer_ingredients_join %>% 
  select(-c(id, name, style, hops_name, malt_name,
            # description,
            glass)) %>% 
  mutate(row = 1:nrow(.)) %>% 
  na.omit()

bi$style_collapsed <- factor(bi$style_collapsed)


# ranger complains about special characters and spaces in ingredient column names. Take them out and replace with empty string.
names(bi) <- tolower(names(bi))
names(bi) <- str_replace_all(names(bi), " ", "")
names(bi) <- str_replace_all(names(bi), "([\\(\\)-\\/')]+)", "")

# Keep 80% for training
bi_train <- sample_n(bi, nrow(bi)*(0.8))

# The rest is for testing
bi_test <- bi %>%
  filter(! (row %in% bi_train$row)) %>%
  dplyr::select(-row)

bi_train <- bi_train %>%
  dplyr::select(-row) %>% 
  select(-`#06300`)

bi_rf <- ranger(style_collapsed ~ ., data = bi_train, importance = "impurity", seed = 11)
```


OOB (out of bag) prediction error is around 58%
    * This calculated from tree samples constructed but not used in training set; these trees become effectively part of test set
```{r}
bi_rf
```


We can compare predicted classification on the test set to their actual style classification.
```{r, echo=TRUE}
pred_bi_rf <- predict(bi_rf, dat = bi_test)
table(bi_test$style_collapsed, pred_bi_rf$predictions)
```


Variable importance
* Interestingly, ABV, IBU, and SRM are all much more important in the random forest than `total_hops` and `total_malt`
```{r, echo=TRUE}

importance(bi_rf)[1:10]
```


How does a CSRF (case-specific random forest) fare?

```{r, echo=TRUE}

bi_csrf <- csrf(style_collapsed ~ ., training_data = bi_train, test_data = bi_test,
                params1 = list(num.trees = 5, mtry = 4),
                params2 = list(num.trees = 2))

csrf_acc <- postResample(bi_csrf, bi_test$style_collapsed)

csrf_acc
```





### Final Thoughts


*Style first, forgiveness later?*

* One reason  seems that beers are generally brewed with style in mind first ("let's make a pale ale") rather than deciding the beer's style after determining its characteristics and idiosyncrasies 
    * Even if the beer turns out more like a sour, and in a blind taste test might be classified as a sour more often than a pale ale, it still gets the label pale ale
    * This makes the style definitions broader and harder to predict



*Future Directions*

* Incorporate flavor profiles for beers sourced/scraped from somewhere
* Implement a GAN to come up with beer names
* More on the hops deep dive: which hops are used most often in which styles?



![](./pour.jpg)





Data Science Musings on Beer

Amanda Dobbyn

July 01, 2017